Use an inequality to solve the problem

One side of a rectangle is 4 imes the other, and the perimeter is not to exceed 150 inches. Find the possible values for X, the length of the shorter side.

Let x , y be the sides of the rectangle.

y=4x.

Perimeter P=2(x+y).

P<150.

2(x+y) < 150.

x+y < 75.

4x+x < 75.

x < 75/5.

x < 15.

The length of the shorter side should not to exceed 15 inches to have perimeter less than 150  inches.